But while the qualitative analysis of history takes years to evolve, math isn’t like that, and there is a quantitative lesson that we ought to absorb today. It stems from this formula, which may look a touch hairy for a Monday morning, but is actually intuitive and deeply informative.
Δ (Debt ratio1) = Debt ratio0 * (r – g)/(1 + g) + p
Like I said, fortify yourself with a gulp of caffeine and stick with me. The debt ratios are just the fiscal debt — the sum of all annual budget deficits — as a share of GDP, right now about 74 percent here in the U.S. and 175 percent in Greece. The letter r is the rate of interest on the debt, g is the nominal growth rate of GDP, and p is any money the government needed to borrow this year to fund its current programs, also known as the “primary deficit.” (For simplicity, I left out the interest on p, which is a small part of the problem and can safely be ignored.)
So, all this formula tells you is that the increase in debt as a share of GDP is last year’s debt ratio times this term we’re about to get into (the bolded one with the r’s and g’s), plus this year’s primary deficit. BTW, that’s also just adding the flow of this year’s budget deficit to the stock of last year’s accumulated debt, as a share of GDP. Those who’d like to go deep into these weeds should consult appendix 3 of this excellent paper by Kogan et al on the topic, as it reviews the history of r’s and g’s in the U.S. as well as the derivation of the formula above.
Now, let’s forget about the math and go to the intuitive place. The increase in the debt should reasonably involve the interest we have to pay on our existing debt plus new borrowing, offset by any growth. That’s all this is saying.
What does any of this have to do with lessons to be learned from Greece?
It is simply this: When interest rates are high relative to growth rates, as is very much the case in Greece, policies that hurt growth will lead to higher, not lower deficits and debt. This is what I called the “dreaded r-g trap” in a book chapter from a few years ago. At the time Spain, Greece, Italy, and Portugal all had interest rates higher than growth rates.
We can and will engage in heated debate regarding the existential issues raised in the introduction about currency unions and moral hazard (the negative incentives engendered by bailing out someone who got themselves in trouble) and so on. But if the interest rate on your debt is higher than your growth rate, you can’t grow your way out of indebtedness.
As austerity measures imposed by their creditors continue to choke the Greek economy, nominal growth rates have been terrible: -1 percent 2015q1 over 2014q1. And that’s not an outlier. The yield on the 10-year Greek government bond was last seen lurking around 11 percent; the 2-year Greek yield has been about twice as high.
This is the unforgiving arithmetic of austerity. As long as (r-g)>0, and in Greece, it’s been a ton > 0, the Greeks will not be able to grow their way out of the mess they’re in, and officials will be back at the bailout table before they know it.
Now, austerians may want to tell a story about how the confidence instilled by harsh fiscal measures will lower the rate of interest (r) which will lead to greater investment and boost g, but go back to the formula. The reason it’s a “dreaded trap” is because “harsh fiscal measures” will tend to lower g, and thus raise your deficits and debt levels, which investors correctly view as unsustainable. That leads to higher r, reduced growth, and more, not less, debt.
I’ll leave you alone about all this in a moment, but consider the American case. What’s lowered the debt ratio across our history has been g (though recently, low r has helped too). As I show in a complementary piece on my blog today, we’ve lowered our debt/GDP ratio the most when we’ve closed the gaps between our actual growth rate and our potential growth rate, the latter being the one associated with full employment, aka a bigger number for g in the formula above.
What’s increased our debt the most has been a) aggressive fiscal spending to fight wars or recessions, and b) the failure, outside of wars and recessions, to raise the revenues necessary to cover the costs of government. I include “b” to be sure to signal to anyone who’s still with me that I do not endorse fiscal profligacy. The failure of the Greeks to collect anything near the taxes they’ve been owed over the years is of course unsustainable. And we too must be careful not to run structural budget deficits, the type that go up even in good times.
But when r is greater than g, as has been the case throughout the crisis in Greece, the economic focus must first be on raising g. Any actions that might lower g must be assiduously avoided.
Of course, economics isn’t politics, and history will have to sort out the latter. But is it really too much to ask that, in the meantime, we mind the arithmetic?